Browse > Article
http://dx.doi.org/10.4134/CKMS.2008.23.1.019

ON THE ORDERED n-PRIME IDEALS IN ORDERED Γ-SEMIGROUPS  

Siripitukdet, Manoj (DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE NARESUAN UNIVERSITY)
Iampan, Aiyared (DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE NARESUAN UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.1, 2008 , pp. 19-27 More about this Journal
Abstract
The motivation mainly comes from the conditions of the (ordered) ideals to be prime or semiprime that are of importance and interest in (ordered) semigroups and in (ordered) $\Gamma$-semigroups. In 1981, Sen [8] has introduced the concept of the $\Gamma$-semigroups. We can see that any semigroup can be considered as a $\Gamma$-semigroup. The concept of ordered ideal extensions in ordered $\Gamma$-semigroups was introduced in 2007 by Siripitukdet and Iampan [12]. Our purpose in this paper is to introduce the concepts of the ordered n-prime ideals and the ordered n-semiprime ideals in ordered $\Gamma$-semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered $\Gamma$-semigroups.
Keywords
(ordered) semigroup; (ordered) $\Gamma$-semigroup; (ordered) ideal; ordered ideal extension; (ordered) prime ideal; (ordered) semiprime ideal; ordered n-prime ideal and ordered n-semiprime ideal;
Citations & Related Records

Times Cited By SCOPUS : 1
연도 인용수 순위
1 Y. I. Kwon and S. K. Lee, The weakly prime ideals of ordered-$\Gamma$-semigroups, Communications of the Korean Mathematical Society 13 (1998), 251-256
2 Y. I. Kwon and S. K. Lee, The weakly semi-prime ideals of po-$\Gamma$-semigroups, Kangweon-Kyungki Mathematical Journal 5 (1997), 135-139
3 S. K. Lee and Y. I. Kwon, A note on weakly prime ideals of ordered semigroups, Mathematica Japonica 50 (1999), 243-246
4 N. K. Saha, On $\Gamma$-semigroup II, Bulletin of the Calcutta Mathematical Society 79 (1987), 331-335
5 M. K. Sen and N. K. Saha, On $\Gamma$-semigroup I, Bulletin of the Calcutta Mathematical Society 78 (1986), 180-186
6 M. K. Sen and N. K. Saha, Orthodox $\Gamma$-semigroups, International Journal of Mathematics and Mathematical Sciences 13 (1990), 527-534   DOI   ScienceOn
7 M. Siripitukdet and A. Iampan, On the least (ordered) semilattice congruences in ordered $\Gamma$-semigroups, Thai Journal of Mathematics 4 (2006), 403-415
8 M. Siripitukdet and A. Iampan, On ordered ideal extensions in po-$\Gamma$-semigroups, Southeast Asian Bulletin of Mathematics, (to appear)
9 A. Iampan and M. Siripitukdet, On minimal and maximal ordered left ideals in po-$\Gamma$-semigroups, Thai Journal of Mathematics 2 (2004), 275-282
10 T. K. Dutta and N. C. Adhikari, On partially ordered $\Gamma$-semigroups, Southeast Asian Bulletin of Mathematics 28 (2004), 1021-1028
11 N. Kehayopulu, On weakly prime ideals of ordered semigroups, Mathematica Japonica 35 (1990), 1051-1056
12 M. K. Sen, On $\Gamma$-semigroups, Proceedings of the International Conference on Algebra and it's Applications, Decker Publication, New York 301